In this section we recall the SDRI model from [1]}, collect all the definitions and hypothesis and state the main results of the paper. Since our model is two-dimensional, unless otherwise stated, all sets we consider are subsets of \(\mathbb {R}^2.\)  We choose the standard basis \(\lbrace {\bf e_1}=(1,0), {\bf e_2}=(0,1)\rbrace \)  in \(\mathbb {R}^2\)  and denote the coordinates of \(x\in \mathbb {R}^2\)  with respect to this basis by \((x_1,x_2).\)  We denote by \(\mathrm {Int}(A)\)  the interior of \(A\subset \mathbb {R}^2.\)  Given a Lebesgue measurable set \(E,\)  we denote by \(\chi _E\)  its characteristic function and by \(|E|\)  its Lebesgue measure. The set
\(E^{(\alpha )}:=\Big \lbrace x\in \mathbb {R}^2:\,\, \lim \limits _{r\rightarrow 0} \frac{|E\cap B_r(x)|}{|B_r(x)|}=\alpha \Big \rbrace ,\qquad \alpha \in [0,1],\) 
